What do you with a sold-out hit? This is a question that has bedeviled the nonprofit Chicago theater for decades.

Consider the conundrum faced right now by the Windy City Playhouse on Irving Park Road. This young theater’s current production, a new play called “Southern Gothic,” is a doozy. I loved it, and so do a lot of Tribune readers. I’m told you’ve bought up pretty much all the tickets through the end of March.

Penned by Leslie Liautaud, “Southern Gothic” is a potboiler that takes place in real time, all during a 1961 dinner party in which political corruption is revealed, marriages unravel and racial tensions erupt. Director David H. Bell’s production is staged environmentally — the remarkable design, by Scott Davis, looks and feels exactly like a real house and yard. There are no theater seats. Rather, you walk around the same space as the actors, as different scenes play out in different rooms.

That cohabitation is what makes the show so great — but it comes at a price. Although the house cost $25,000 to build (and looks like it should have cost a lot more) “Southern Gothic” can only accommodate 28 people per performance. That limits the amount of money coming in at the box office. Windy City is a frugal nonprofit, though, and consistently sold-out houses at a non-discounted $65 or so (including cocktails, remarkably) are enough to keep things ticking over, especially since the theater is doing seven performances a week, and is about to add an eighth. Very few off-Loop theaters stage eight shows a week.

Today, the Windy City Playhouse is announcing an extension through Memorial Day weekend (don’t wait around if you want to go). That is possible because, after several years of trial and error, Windy City’s artistic director Amy Rubenstein decided last year not to announce her performance dates a year in advance. That has allowed her the flexibility to run hit shows (like “Southern Gothic”) for longer and close less successful shows more quickly and move on to the next. This is more like a commercial venue, but then Windy City also is a theater with a populist mission

“I think we finally figured out that our place in this theater world in Chicago is to connect ordinary people to the arts,” Rubenstein said. “Not just the people dedicated to the theater but ordinary people.”

If you saw “Becky Shaw” (which was terrific), you saw Windy City’s first stabs at an immersive environment. But “Southern Gothic” goes a lot further. “I think,” Rubenstein said, “that proscenium-style theater is just not enough stimulation for everybody. I’d always wanted to give an audience the same feeling as an actor auditioning for a show. That same excitement. So, basically, we just decided to put everyone in the show.”

It works remarkably well. Rubenstein said that she hopes “Southern Gothic” can turn what has always been the summer doldrums in Old Irving Park into a successful further extension. But come Labor Day, she runs into a dilemma. “We still want to have a season next year,” she said.

You might wonder why. If you have a sell-out, why not just keep it going like they do on Broadway? But here’s the counter-argument. Lots of those new audience members — you, maybe — are going up to Rubenstein and telling her that they’d like to become subscribers to the theater where they had such a good time. So she worries that if “Southern Gothic” just runs and runs, then that opportunity for audience building is not being fully exploited.

A fascinating — and happy — dilemma, no?

The ideal solution, of course, is to move the show elsewhere and run two shows at once. And that is what is being explored, although the limited seating capacity remains an issue. Could it be made bigger without spoiling the experience? Only one way to find out.

At least all Windy City needs is a warehouse with bathrooms; that’s the plus of a hugely fun theatrical experience that doesn’t need a theater.